Model Kredibilitas Bühlmann-Straub untuk Frekuensi Klaim Berdistribusi Binomial Negatif–Lindley

Ikhsan Maulidi, Uswah Uswah, Rini Oktavia, Alim Misbullah, Vina Apriliani

Abstract


The credibility theory is one of the tools that can be used to determine risk-based premiums. One approach that can be used is the best accuracy approach such as Bühlmann-Straub. We study the parametric Bühlmann-Straub credibility model in which the claim frequency data is assumed to follow the Negative-Lindley (NB-L) Binomial distribution. Determination of the Bühlmann-Straub parameter is determined by using the basic rules in probability theory. From the study that has been carried out, an explicit equation has been obtained to determine the credibility premium of Bühlmann-Straub. A simulation of the application of the model to the data was also provided by assuming the data follows the NB-L distribution. The NB-L distribution parameters were estimated using the momen method and maximum likelihood estimation. From the simulation, it is found that the data used had a high credibility factor value which implies the data can be considered primely for estimating future premiums.

Keywords


Bühlmann-Straub credibility; Negative Binomial-Lindley; premium; credibility; maximum Likelihood estimation; momen method

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References


H. Bühlmann and A. Gisler, A Course in Credibility Theory and Its Applications. Springer Science & Business Media, 2006.

A. R. Effendie, Teori Risiko Aktuaria dengan Software R. Yogyakarta: UGM Press, 2019.

J. A. Green, “Too many zeros and/or highly skewed? a tutorial on modelling health behaviour as count data with Poisson and Negative Binomial regression,” Heal. Psychol. Behav. Med., vol. 9, no. 1, pp. 436–455, 2021, doi: 10.1080/21642850.2021.1920416.

H. Zamani and N. Ismail, “Negative binomial-Lindley distribution and its application,” J. Math. Stat., vol. 6, no. 1, pp. 4–9, 2010, doi: 10.3844/jmssp.2010.4.9.

L. M. Wen, W. Wang, and J. L. Wang, “The credibility premiums for exponential principle,” Acta Math. Sin. Engl. Ser., vol. 27, no. 11, pp. 2217–2228, 2011, doi: 10.1007/s10114-011-9198-4.

A. Hassan Zadeh and D. A. Stanford, “Bayesian and Bühlmann credibility for phase-type distributions with a univariate risk parameter,” Scand. Actuar. J., vol. 2016, no. 4, pp. 338–355, 2016.

T. M. Karina, S. Nurrohmah, and I. Fithriani, “Buhlmann credibility model in predicting claim frequency that follows heterogeneous Weibull count distribution,” in Journal of Physics: Conference Series, 2019, vol. 1218, no. 1, p. 012041. doi: 10.1088/1742-6596/1218/1/012041.

I. Maulidi and V. Apriliani, “Model kredibilitas Bühlmann dengan frekuensi klaim berdistribusi Binomial Negatif-Lindley,” Limits J. Math. Its Appl., vol. 18, no. 1, pp. 71–78, 2021, doi: 10.12962/limits.v18i1.6690.

I. Maulidi, W. Erliana, A. D. Garnadi, S. Nurdiati, and I. G. P. Purnaba, “Penghitungan kredibilitas dengan pustaka actuar dalam R,” J. Math. Its Appl., vol. 16, no. 2, pp. 45–52, 2017, doi: 10.29244/jmap.16.2.45-52.

S. Ghahramani, Fundamentals of Probability. New York (US): Prentice Hall, 2005.

L. J. Bain and M. Engelhardt, Introduction to Probability and Mathematical Statistics. California: Duxbury Press, 1992.

M. E. Ghitany, B. Atieh, and S. Nadarajah, “Lindley distribution and its application,” Math. Comput. Simul., vol. 78, no. 4, pp. 493–506, 2008, doi: 10.1016/j.matcom.2007.06.007.

I. S. Zahra, “Perhitungan Premi dengan Menggunakan Model Kredibilitas Buhlmann dan Buhlmann Straub,” Institut Pertanian Bogor, 2019.




DOI: http://dx.doi.org/10.12962/limits.v20i1.12618

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